What is the integral of 4sin(2x+3) ?

The integral of 4sin(2x+3) is -2cos(2x+3)+C

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integral of 4sin(2x+3)

\int 4 sin (2 x + 3) d x

- 2 cos (2 x + 3) + C

Solution steps

\int 4 sin (2 x + 3) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int sin (2 x + 3) d x

Apply u-substitution

: \int sin (u) \frac{1}{2} d u

= 4 \cdot \int sin (u) \frac{1}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= 4 \cdot \frac{1}{2} (- cos (u))

Substitute back

u = 2 x + 3

= 4 \cdot \frac{1}{2} (- cos (2 x + 3))

Simplify

4 \cdot \frac{1}{2} (- cos (2 x + 3)) : - 2 cos (2 x + 3)

= - 2 cos (2 x + 3)

Add a constant to the solution

= - 2 cos (2 x + 3) + C

y = e^{2 x} arcsin (x)

16 cos (2 x)

y - y^{^{''}} = (1 + π^{2}) sin (π x)

\int \frac{1}{1 + 11 x} d x

y = (5 x + 1)^{4} (4 x + 3)^{- 2}

What is the integral of 4sin(2x+3) ?
The integral of 4sin(2x+3) is -2cos(2x+3)+C